How do I regain control of my hacked Apple Account?

You need to change the password on your Apple ID account. See this support document if you believe your Apple ID to be compromised. If you think your Apple Account has been compromised - Apple Support

However, just having access to your Apple ID account would not allow for remote control of your Apple devices, and unless you jailbroke your devices, they cannot be remote controlled.

What steps have you already taken to re-secure your Apple Account, as the usual suggestions should have already resolved this?

That you have tried those steps might mean something else is going on here, whether some other issue or attack, or maybe the adversary is lying, or is getting information from somebody else involved.